Mitch McConnell Campaigns on Clout Despite Anti-Insider Mood

HAZARD, Ky.—Mitch McConnell, the top Republican in the U.S. Senate, is building his re-election campaign around a concept that hasn't been heard much recently: Vote for me—I'm powerful.

In a February swing through southeastern Kentucky, Mr. McConnell touted his central role in inserting a pilot program for hemp growers into a recent farm bill and in fighting with the Obama administration over proposed rules on coal-fired power...